How to implement an artificial network that outputs an integer within a range?
First of all, sigmoid does not output 0 or 1, it outputs any real number in the range between 0 and 1.

Furthermore, normal neural networks doesn't output binary values, unless the output layer uses the step function as activation function (which is rare).

I'm not really sure if you want the NN to be a classifier or regressor, but it sounds like you want a regressor.

Regression is when you are interested in the value of the output nevron(s) itself. A simple example is if you want the network to predict the sum of two input neurons.

If you want to change the network from a classifier to a regressor you should probably reduce the number of neurons in the output layer to 1, and change the activation function of that neuron from softmax to the identity function (f(x)=x; which is the same as no activation function at all).

Hope this helps. Provide some more details if this didn't answer your question.